Learning in the framework of fuzzy lattices

A basis for rigorous versatile learning is introduced theoretically, that i s the framework of fuzzy lattices or framework for short, which proposes a synergetic combination of fuzzy set theory and lattice theory. A fuzzy latt ice emanates from a conventional mathematical lattice by fuzzifying the inc lusion order relation. Learning in the FL-framework can be effected by hand ling families of intervals, where an interval is treated as a single entity /block the way explained here. Illustrations are provided in a lattice defi ned on the unit-hypercube where a lattice interval corresponds to a convent ional hyperbox, A specific scheme for learning by clustering is presented, namely sigma-fuzzy lattice learning scheme or sigma-FLL (scheme) for short, inspired from the adaptive resonance theory (ART), Learning by the sigma-F LL is driven by an inclusion measure a of the corresponding Cartesian produ ct to be introduced here. We delineate a comparison of the sigma-FLL scheme with various neural-fuzzy and other models. Applications are shown to one medical data set and two benchmark data sets, where sigma-FLL's capacity fo r treating efficiently real numbers as well as lattice-ordered symbols sepa rately or jointly is demonstrated. Due to its efficiency and wide scope of applicability the sigma-FLL scheme emerges as a promising learning scheme.